A New Approach to the Study of Fixed Point Theory for Simulation Functions

被引：301

作者：

Khojasteh, Farshid ^{[1
]}

Shukla, Satish ^{[2
]}

Radenovic, Stojan ^{[3
]}

机构：

[1] Islamic Azad Univ, Dept Math, Arak Branch, Arak, Iran

[2] Shri Vaishnav Inst Technol & Sci, Dept Appl Math, Indore 453331, India

[3] Univ Belgrade, Fac Mech Engn, Beograd 11120, Serbia

来源：

FILOMAT | 2015年 / 29卷 / 06期

关键词：

Contraction mapping; Simulation function; Z-contraction; Fixed point; MAPPINGS; SPACES;

D O I：

10.2298/FIL1506189K

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (X, d) be a metric space and T : X -> X be a mapping. In this work, we introduce the mapping zeta : [0, infinity) x [0, infinity) -> R, called the simulation function and the notion of Z-contraction with respect to zeta which generalize the Banach contraction principle and unify several known types of contractions involving the combination of d(Tx, Ty) and d(x, y) : The related fixed point theorems are also proved.

引用

页码：1189 / 1194

页数：6

共 9 条

[1]

Banach S., 1922, Fund. math, V3, P133, DOI [10.4064/fm-3-1-133-181, DOI 10.4064/FM-3-1-133-181]

[2] ON NONLINEAR CONTRACTIONS [J].

BOYD, DW ;

WONG, JSW .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 20 (02) :458-&

[3] SOLUTION BY ITERATION OF NONLINEAR FUNCTIONAL EQUATIONS IN BANACH SPACES [J].

BROWDER, FE ;

PETRYSHYN, WV .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 72 (03) :571-+

[4] Discussions on Recent Results for α-ψ-Contractive Mappings [J].

Hussain, N. ;

Kutbi, M. A. ;

Khaleghizadeh, S. ;

Salimi, P. .

ABSTRACT AND APPLIED ANALYSIS, 2014,

[5] Comparison Functions and Fixed Point Results in Partial Metric Spaces [J].

Hussain, Nawab ;

Kadelburg, Zoran ;

Radenovic, Stojan ;

Al-Solamy, Falleh .

ABSTRACT AND APPLIED ANALYSIS, 2012,

[6] Some new common fixed point results for generalized contractive multi-valued non-self-mappings [J].

Khojasteh, Farshid ;

Rakocevic, Vladimir .

APPLIED MATHEMATICS LETTERS, 2012, 25 (03) :287-293

[7] FIXED-POINT THEOREMS FOR MULTIVALUED MAPPINGS ON COMPLETE METRIC-SPACES [J].

MIZOGUCHI, N ;

TAKAHASHI, W .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 141 (01) :177-188

[8] COMPARISON OF VARIOUS DEFINITIONS OF CONTRACTIVE MAPPINGS [J].

RHOADES, BE .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 226 (FEB) :257-290

[9] Some theorems on weakly contractive maps [J].

Rhoades, BE .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (04) :2683-2693

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