Let <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2455397pt" id="M1" height="9.25986pt" version="1.1" viewBox="-0.0498162 -9.01432 12.4177 9.25986" width="12.4177pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g198-19" d="M852 669C820 657 792 643 768 628C705 667 627 687 547 687C310 687 154 548 154 412C154 332 212 282 296 282C434 282 515 426 523 557H503C474 402 410 312 298 312C241 312 195 352 195 408C195 535 341 657 546 657C613 657 683 644 738 609C640 538 574 431 486 271C374 71 314 16 189 16C118 16 69 60 69 95H71C78 84 93 83 101 83C129 83 144 106 144 131C144 160 121 179 93 179C60 179 34 151 34 108C34 42 100 -15 207 -15C364 -15 491 73 603 304C614 297 639 293 650 293C681 293 683 254 683 245C683 181 599 150 599 70C599 21 645 -12 692 -12C747 -12 804 30 868 103L851 119C789 52 741 18 706 18C685 18 674 29 674 52C674 92 750 157 750 226C750 257 727 287 696 310V312C812 315 876 394 876 473C876 525 849 577 793 612C812 627 832 639 859 650L852 669ZM814 486C814 417 765 345 686 337C669 348 649 354 626 354C673 451 708 533 766 588C799 561 814 525 814 486Z"/></g></svg> denote the family of functions <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.9435pt" id="M2" height="14.5524pt" version="1.1" viewBox="-0.0498162 -10.6089 108.93 14.5524" width="108.93pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-103" d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z"/></g><g transform="matrix(.013,0,0,-0.013,8.352,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.013,0,0,-0.013,12.85,0)"><path id="g113-123" d="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z"/></g><g transform="matrix(.013,0,0,-0.013,19.325,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g><g transform="matrix(.013,0,0,-0.013,27.455,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g><g transform="matrix(.013,0,0,-0.013,38.718,0)"><use xlink:href="#g113-123"/></g><g transform="matrix(.013,0,0,-0.013,48.099,0)"><path id="g117-36" d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"/></g><g transform="matrix(.013,0,0,-0.013,58.635,.007)"><path id="g119-65" d="M697 -46L668 -39C637 -126 611 -142 545 -142H163L474 298L206 694H483C558 694 584 688 600 668C615 651 627 625 639 580L667 585L655 739H70V714L378 254L53 -203V-228H655L697 -46Z"/></g><g transform="matrix(.0091,0,0,-0.0091,68.422,-6.394)"><path id="g50-30" d="M1000 227C1000 351 905 451 780 451C658 451 590 380 530 279C465 385 388 451 261 451C168 451 38 376 38 210C38 98 121 -12 261 -12C381 -12 448 59 508 160C573 53 652 -12 780 -12C879 -12 1000 64 1000 227ZM485 199C434 109 370 25 271 25C188 25 133 117 133 241C133 355 189 414 249 414C357 414 426 302 485 199ZM903 204C903 70 852 25 790 25C681 25 611 136 552 240C603 330 669 414 768 414C855 414 903 321 903 204Z"/></g><g transform="matrix(.0091,0,0,-0.0091,68.422,3.784)"><path id="g50-111" d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"/></g><g transform="matrix(.0091,0,0,-0.0091,73.081,3.784)"><path id="g54-34" d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z"/></g><g transform="matrix(.0091,0,0,-0.0091,78.641,3.784)"><path id="g50-51" d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"/></g><g transform="matrix(.013,0,0,-0.013,85.805,0)"><path id="g113-98" d="M483 97L471 123C436 91 401 65 392 65C388 65 384 74 390 106C414 239 444 378 457 429L455 433C444 433 429 436 416 439C392 444 368 448 344 448C281 448 204 415 152 376C71 315 23 205 23 103C23 21 57 -12 85 -12C114 -12 149 6 185 34C231 70 285 119 329 183H331L309 81C292 0 308 -12 326 -12C350 -12 421 24 483 97ZM374 387C370 363 356 291 345 261C315 193 181 50 139 50C124 50 110 71 110 118C110 224 153 331 218 379C238 394 271 402 301 402C329 402 359 394 374 387Z"/></g><g transform="matrix(.0091,0,0,-0.0091,91.798,3.132)"><use xlink:href="#g50-111"/></g><g transform="matrix(.013,0,0,-0.013,96.973,0)"><use xlink:href="#g113-123"/></g><g transform="matrix(.0091,0,0,-0.0091,103.448,-5.741)"><use xlink:href="#g50-111"/></g></svg> of bounded boundary rotation so that <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.4294pt" id="M3" height="14.8655pt" version="1.1" viewBox="-0.0498162 -11.4361 71.6007 14.8655" width="71.6007pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-83" d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"/></g><g transform="matrix(.013,0,0,-0.013,8.151,0)"><path id="g113-102" d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"/></g><g transform="matrix(.013,0,0,-0.013,13.534,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,18.032,0)"><use xlink:href="#g113-103"/></g><g transform="matrix(.0091,0,0,-0.0091,26.384,-5.741)"><path id="g50-31" d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"/></g><g transform="matrix(.013,0,0,-0.013,30.179,0)"><use xlink:href="#g113-41"/></g><g transform="matrix(.013,0,0,-0.013,34.677,0)"><use xlink:href="#g113-123"/></g><g transform="matrix(.013,0,0,-0.013,41.152,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,45.65,0)"><use xlink:href="#g113-42"/></g><g transform="matrix(.013,0,0,-0.013,53.78,0)"><path id="g117-92" d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z"/></g><g transform="matrix(.013,0,0,-0.013,65.043,0)"><path id="g113-49" d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"/></g></svg> in the open unit disk <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.26807pt" id="M4" height="11.5564pt" version="1.1" viewBox="-0.0498162 -9.28833 84.4725 11.5564" width="84.4725pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g197-32" d="M633 662H589V197C589 69 451 30 347 30C317 30 258 37 231 50V662H65V196C65 45 219 -14 348 -14C483 -14 633 44 633 201V662ZM187 67C140 104 109 130 109 196V618H187V67Z"/></g><g transform="matrix(.013,0,0,-0.013,12.706,0)"><use xlink:href="#g117-34"/></g><g transform="matrix(.013,0,0,-0.013,23.969,0)"><path id="g113-124" d="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z"/></g><g transform="matrix(.013,0,0,-0.013,28.48,0)"><use xlink:href="#g113-123"/></g><g transform="matrix(.013,0,0,-0.013,38.587,0)"><path id="g113-59" d="M116 412C83 412 59 388 59 355C59 321 83 297 115 297S170 321 170 355C170 388 147 412 116 412ZM114 -12C147 -12 171 11 171 46C171 78 147 103 115 103C84 103 60 78 60 46C60 11 84 -12 114 -12Z"/></g><g transform="matrix(.013,0,0,-0.013,45.183,0)"><path id="g113-9" d="M162 -163V703H101V-163H162Z"/></g><g transform="matrix(.013,0,0,-0.013,48.602,0)"><use xlink:href="#g113-123"/></g><g transform="matrix(.013,0,0,-0.013,55.077,0)"><use xlink:href="#g113-9"/></g><g transform="matrix(.013,0,0,-0.013,62.128,0)"><path id="g117-91" d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z"/></g><g transform="matrix(.013,0,0,-0.013,73.391,0)"><path id="g113-50" d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"/></g><g transform="matrix(.013,0,0,-0.013,79.631,0)"><path id="g113-126" d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z"/></g></svg>. We obtain sharp bounds for Toeplitz determinants whose elements are the coefficients of functions <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.42947pt" id="M5" height="12.7178pt" version="1.1" viewBox="-0.0498162 -9.28833 34.9484 12.7178" width="34.9484pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-103"/></g><g transform="matrix(.013,0,0,-0.013,11.984,0)"><path id="g117-173" d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z"/></g><g transform="matrix(.013,0,0,-0.013,22.48,0)"><use xlink:href="#g198-19"/></g></svg>.

V. Radhika

S. Sivasubramanian

G. Murugusundaramoorthy

Jay M. Jahangiri

Toeplitz Matrices Whose Elements Are the Coefficients of Functions with Bounded Boundary Rotation

Here, we present the new method of approximate conformal mapping of the unit disk to a one-connected domain with smooth boundary without auxiliary constructions and iterations. The mapping function is a Taylor polynomial. The method is applicable to elasticity problems solution.

Pyotr N. Ivanshin

Elena A. Shirokova

Approximate Conformal Mappings and Elasticity Theory

We study some relative growth properties of entire functions with respect to another entire function on the basis of generalized relative type and generalized relative weak type.

Sanjib Kumar Datta

Tanmay Biswas

Debasmita Dutta

Generalized Relative Type and Generalized Weak Type of Entire Functions

The aim of this paper is to prove the existence and uniqueness of a common fixed point for a pair of mappings satisfying certain rational contraction conditions in complex valued <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M2" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-99"/></g></svg>-metric space. The obtained results generalize and extend some of the well-known results in the literature.

Anil Kumar Dubey

Complex Valued <svg  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"   style="vertical-align:-0.2063999pt" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-99" d="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" /></g></svg>-Metric Spaces and Common Fixed Point Theorems under Rational Contractions

The parqueting-reflection method is applied to a nonregular domain and the harmonic Green function for the half hexagon is constructed. The related Dirichlet problem for the Poisson equation is solved explicitly.

Bibinur Shupeyeva

Dirichlet Problem for Complex Poisson Equation in a Half Hexagon Domain

We establish sharp estimates for Green&#x2019;s functions of cone-type planar domains. Our work generalizes all estimates given by Zhao in 1988 and Selmi in 2000. Our principal idea is to use conformal mappings.

Mohamed Amine Ben Boubaker

Mohamed Selmi

Sharp Estimates for Green&#x2019;s Functions of Cone-Type Planar Domains

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Journal of Complex Analysis