TY - JOUR T1 - Fixed point theorem for a kind of \'{C}iri\'{c} type contractions in complete metric spaces AU - Suzuki, Tomonari PY - 2018 DA - March DO - 10.31197/atnaa.375870 JF - Advances in the Theory of Nonlinear Analysis and its Application JO - ATNAA PB - Erdal KARAPINAR WT - DergiPark SN - 2587-2648 SP - 33 EP - 41 VL - 2 IS - 1 LA - en AB - We prove a fixed point theoremfor a kind of C'iric' type contractionsin complete metric spaces.In order to demonstrate the assumption of the fixed point theorem,we give an example.We also clarify the mathematical structure ofsome fixed point theoremproved by Mınak-Helvacı-Altun andWardowski-Dung independently. KW - Fixed point KW - $F$-contraction KW - contractive condition CR - F. E. Browder, {\it On the convergence of successive approximations for nonlinear functional equations}, Nederl.\ Akad.\ Wetensch.\ Proc.\ Ser.\ A 71=Indag.\ Math.\ 30 (1968), 27--35. % MR0230180 % 10.1016/S1385-7258(68)50004-0 CR - Lj. B. \'Ciri\'c, {\it A new fixed-point theorem for contractive mappings}, Publ.\ Inst.\ Math.\ (Beograd), 30 (1981), 25--27. % MR0672538 CR - M. Heged\"{u}s and T. Szil\'{a}gyi, {\it Equivalent conditions and a new fixed point theorem in the theory of contractive type mappings}, Math.\ Japon., 25 (1980), 147--157. % MR0571276 CR - J. Jachymski, {\it Equivalent conditions and the Meir-Keeler type theorems}, J.\ Math.\ Anal.\ Appl., 194 (1995), 293--303. % MR1353081 % 10.1006/jmaa.1995.1299 CR - J. Matkowski, {\it Fixed point theorems for contractive mappings in metric spaces}, \v Casopis P\v est.\ Mat., 105 (1980), 341--344. % MR0597909 CR - G. M\i{}nak, A. Helvac\i{} and \.{I}. Altun, {\it \'{C}iri\'{c} type generalized $F$-contractions on complete metric spaces and fixed point results}, Filomat, 28 (2014), 1143--1151. % MR3360088 CR - T. Suzuki, {\it Discussion of several contractions by Jachymski's approach}, Fixed Point Theory Appl., 2016, 2016:91. % MR3548683 % 10.1186/s13663-016-0581-9 CR - T. Suzuki, {\it Characterizations of contractive conditions by using convergent sequences}, Fixed Point Theory Appl., 2017, 2017:30. % 10.1186/s13663-017-0623-y CR - T. Suzuki, {\it A generalization of Heged\"{u}s-Szil\'{a}gyi's fixed point theorem in complete metric spaces}, Fixed Point Theory Appl., 2018, 2018:1. % 10.1186/s13663-017-0625-9 CR - D. Wardowski, {\it Fixed points of a new type of contractive mappings in complete metric spaces}, Fixed Point Theory Appl., 2012, 2012:94. % MR2949666 CR - D. Wardowski and N. V. Dung, {\it Fixed points of $F$-weak contractions on complete metric spaces}, Demonstr.\ Math., 47 (2014), 146--155. % MR3200192 UR - https://doi.org/10.31197/atnaa.375870 L1 - https://dergipark.org.tr/tr/download/article-file/596066 ER -