Araştırma Makalesi

Fixed point theorem for a kind of \'{C}iri\'{c} type contractions in complete metric spaces

Cilt: 2 Sayı: 1 25 Mart 2018
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Fixed point theorem for a kind of \'{C}iri\'{c} type contractions in complete metric spaces

Abstract

We prove a fixed point theorem  for a kind of C'iric' type contractions  in complete metric spaces. In order to demonstrate the assumption of the fixed point theorem,  we give an example. We also clarify the mathematical structure of  some fixed point theorem  proved by Mınak-Helvacı-Altun and  Wardowski-Dung independently.

Keywords

Kaynakça

  1. 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
  2. Lj. B. \'Ciri\'c, {\it A new fixed-point theorem for contractive mappings}, Publ.\ Inst.\ Math.\ (Beograd), 30 (1981), 25--27. % MR0672538
  3. 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
  4. 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
  5. J. Matkowski, {\it Fixed point theorems for contractive mappings in metric spaces}, \v Casopis P\v est.\ Mat., 105 (1980), 341--344. % MR0597909
  6. 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
  7. 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
  8. T. Suzuki, {\it Characterizations of contractive conditions by using convergent sequences}, Fixed Point Theory Appl., 2017, 2017:30. % 10.1186/s13663-017-0623-y

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yazarlar

Yayımlanma Tarihi

25 Mart 2018

Gönderilme Tarihi

8 Ocak 2018

Kabul Tarihi

21 Ocak 2018

Yayımlandığı Sayı

Yıl 2018 Cilt: 2 Sayı: 1

Kaynak Göster

Cited By