On (ϕ, ψ)-Metric Spaces with Applications

The aim of this article is to introduce the notion of a ϕ,ψ-metric space, which extends the metric space concept. In these spaces, the symmetry property is preserved. We present a natural topology τϕ,ψ in such spaces and discuss their topological properties. We also establish the Banach contraction principle in the context of ϕ,ψ-metric spaces and we illustrate the significance of our main theorem by examples. Ultimately, as applications, the existence of a unique solution of Fredholm type integral equations in one and two dimensions is ensured and an example in support is given.

[1]  Hassen Aydi,et al.  Coupled fixed point results for (ψ, φ)-weakly contractive condition in ordered partial metric spaces , 2011, Comput. Math. Appl..

[2]  Manuel De la Sen,et al.  Solution of Nonlinear Integral Equation via Fixed Point of Cyclic $$\alpha _{L}^{ \psi }$$αLψ-Rational Contraction Mappings in Metric-Like Spaces , 2020, Bulletin of the Brazilian Mathematical Society, New Series.

[3]  Hassen Aydi,et al.  Best Proximity Points of -Cyclic Contractions with Property UC , 2020 .

[4]  Parvez N. Guzdar,et al.  An electromagnetic integral equation: Application to microtearing modes , 1983 .

[5]  H. A. Hammad,et al.  A Coupled Fixed Point Technique for Solving Coupled Systems of Functional and Nonlinear Integral Equations , 2019, Mathematics.

[6]  Hassen Aydi,et al.  Double Controlled Metric Type Spaces and Some Fixed Point Results , 2018, Mathematics.

[7]  Bessem Samet,et al.  A generalized metric space and related fixed point theorems , 2015 .

[8]  Hassen Aydi,et al.  Fixed point results via a Hausdorff controlled type metric , 2020 .

[9]  Manuel De la Sen,et al.  A Solution of Fredholm Integral Equation by Using the Cyclic η s q -Rational Contractive Mappings Technique in b-Metric-Like Spaces , 2019, Symmetry.

[10]  S. Gähler,et al.  2-metrische Räume und ihre topologische Struktur†‡‡ , 1963 .

[11]  Wasfi Shatanawi,et al.  Coupled Fixed Point Theorems Employing CLR-Property on V -Fuzzy Metric Spaces , 2020, Mathematics.

[12]  Hassen Aydi,et al.  Controlled Metric Type Spaces and the Related Contraction Principle , 2018, Mathematics.

[13]  D. N. Sidorov,et al.  Solving the hammerstein integral equation in the irregular case by successive approximations , 2010 .

[14]  Wasfi Shatanawi,et al.  New results on modified intuitionistic generalized fuzzy metric spaces by employing E.A property and common E.A property for coupled maps , 2020, J. Intell. Fuzzy Syst..

[15]  Hassen Aydi,et al.  Fixed Point Results for Multi-Valued Contractions in b−Metric Spaces and an Application , 2019, Mathematics.

[16]  M. I. Berenguer,et al.  Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation , 2009 .

[17]  Bessem Samet,et al.  On a new generalization of metric spaces , 2018, Journal of Fixed Point Theory and Applications.

[18]  Ivar Fredholm.  Sur une classe d’équations fonctionnelles , 1903 .

[19]  Hassen Aydi,et al.  ON H+Type Multivalued Contractions and Applications in Symmetric and Probabilistic Spaces , 2019, Mathematics.

[20]  Muhammad Arshad,et al.  Hybrid Ćirić Type Graphic Υ, Λ-Contraction Mappings with Applications to Electric Circuit and Fractional Differential Equations , 2020, Symmetry.

[21]  Hassen Aydi,et al.  Partial Hausdorff metric and Nadlerʼs fixed point theorem on partial metric spaces , 2012 .

[22]  Hassen Aydi,et al.  A Nadler-type fixed point theorem in dislocated spaces and applications , 2018 .

[23]  Ronald Fagin,et al.  Comparing top k lists , 2003, SODA '03.

[24]  S. G. Matthews,et al.  Partial Metric Topology , 1994 .

[25]  Hassen Aydi,et al.  -Meir-Keeler Contraction Mappings in Generalized -Metric Spaces , 2018 .

[26]  Denis Sidorov,et al.  Existence and blow-up of Kantorovich principal continuous solutions of nonlinear integral equations , 2014 .