Ulam-Hyers Stability Results for Fixed Point Problems via --Contractive Mapping in ()-Metric Space

We will investigate some existence, uniqueness, and Ulam-Hyers stability results for fixed point problems via --contractive mapping of type-() in the framework of -metric spaces. The presented theorems extend, generalize, and unify several results in the literature, involving the results of Samet et al. (2012).

[1]  D. H. Hyers On the Stability of the Linear Functional Equation. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[2]  S. Ulam Problems in modern mathematics , 1964 .

[3]  K. L. Singh,et al.  Fixed-point theorems for contractive-type mappings , 1979 .

[4]  S. Czerwik,et al.  Contraction mappings in $b$-metric spaces , 1993 .

[5]  Y. Berezansky,et al.  Functional Analysis: Vol. I , 1996 .

[6]  S. Czerwik,et al.  Nonlinear set-valued contraction mappings in b-metric spaces , 1998 .

[7]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[8]  Ioan A. Rus,et al.  REMARKS ON ULAM STABILITY OF THE OPERATORIAL EQUATIONS , 2009 .

[9]  M. Boriceanu FIXED POINT THEORY FOR MULTIVALUED GENERALIZED CONTRACTION ON A SET WITH TWO b-METRICS , 2009 .

[10]  A. Petruşel,et al.  Fixed Point Theorems for Some Multivalued Generalized Contractions in B-Metric Spaces , 2010 .

[11]  Muhammad Usman,et al.  Fully Nonlinear Boundary Value Problems with Impulse , 2011 .

[12]  J.-C. Yao,et al.  ULAM-HYERS STABILITY FOR OPERATORIAL EQUATIONS AND INCLUSIONS VIA NONSELF OPERATORS , 2011 .

[13]  Krzysztof Ciepliński,et al.  A fixed point approach to the stability of functional equations in non-Archimedean metric spaces , 2011 .

[14]  Ulam-Hyers Stability for Operatorial Equations , 2011 .

[15]  Zsolt Páles,et al.  A fixed point approach to stability of functional equations , 2011 .

[16]  Hassen Aydi,et al.  A fixed point theorem for set-valued quasi-contractions in b-metric spaces , 2012, Fixed Point Theory and Applications.

[17]  P. Gǎvruţa,et al.  Fixed Points and Generalized Hyers-Ulam Stability , 2012 .

[18]  S. Moradi,et al.  A COMMON FIXED POINT FOR WEAK -CONTRACTIONS ON b-METRIC SPACES , 2012 .

[19]  Bessem Samet,et al.  Fixed point theorems for α–ψ-contractive type mappings , 2012 .

[20]  Zoran Kadelburg,et al.  Comparison Functions and Fixed Point Results in Partial Metric Spaces , 2012 .

[21]  ULAM-HYERS-RASSIAS STABILITY FOR SET INTEGRAL EQUATIONS , 2012 .

[22]  A. Petruşel,et al.  Ulam-Hyers stability for partial differential inclusions , 2012 .

[23]  J. Brzdȩk,et al.  A fixed point theorem and the Hyers–Ulam stability in non-Archimedean spaces , 2013 .

[24]  Luigi Ambrosio,et al.  Lectures on analysis in metric spaces , 2013 .