Hybrid Multivalued Type Contraction Mappings in αK-Complete Partial b-Metric Spaces and Applications

In this paper, we initiate the notion of generalized multivalued ( α K * , Υ , Λ ) -contractions and provide some new common fixed point results in the class of α K -complete partial b-metric spaces. The obtained results are an improvement of several comparable results in the existing literature. We set up an example to elucidate our main result. Moreover, we present applications dealing with the existence of a solution for systems either of functional equations or of nonlinear matrix equations.

[1]  O. Popescu.  Some new fixed point theorems for α-Geraghty contraction type maps in metric spaces , 2014, Fixed Point Theory and Applications.

[2]  Hassen Aydi,et al.  Fixed point results for generalized α − ψ-Suzuki-contractions in quasi-b-metric-like spaces , 2018 .

[3]  S. Nadler.  Multi-valued contraction mappings. , 1969 .

[4]  Katrin Baumgartner.  Functional Analysis With Current Applications In Science Technology And Industry , 2016 .

[5]  C. Vetro,et al.  Common fixed points for multivalued generalized contractions on partial metric spaces , 2014 .

[6]  Further generalizations of the Banach contraction principle , 2014 .

[8]  S. Banach.  Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , 1922 .

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

[10]  Liu Zeqing,et al.  SOME EXISTENCE THEOREMS FOR FUNCTIONAL EQUATIONS ARISING IN DYNAMIC PROGRAMMING , 2006 .

[11]  Hassen Aydi,et al.  Fixed points for generalized (α,ψ)-contractions on generalized metric spaces , 2014, Journal of Inequalities and Applications.

[12]  Peyman Salimi,et al.  Some fixed point results for (α,β)-(ψ,Φ)-contractive mappings , 2014 .

[13]  Bessem Samet,et al.  A new generalization of the Banach contraction principle , 2014, Journal of Inequalities and Applications.

[14]  M. Arshad,et al.  Common fixed point results for generalized $$\alpha _{*}$$α∗-$$\psi $$ψ-contraction multivalued mappings in b-metric spaces , 2017 .

[15]  H. Pathak,et al.  Fixed point theorems for compatible mappings of type (P) and applications to dynamic programming , 1995 .

[16]  Shih-sen Chang,et al.  Some fixed point theorems concerning (ψ,ϕ )-type contraction in complete metric spaces , 2016 .

[17]  P. C. Bhakta,et al.  Some existence theorems for functional equations arising in dynamic programming, II , 1984 .

[18]  Erdal Karapınara.  α-ψ-Geraghty contraction type mappings and some related fixed point results , 2014 .

[19]  Hassen Aydi,et al.  NEW FIXED POINT RESULTS FOR MULTI-VALUED MAPS VIA MANAGEABLE FUNCTIONS AND AN APPLICATION ON A BOUNDARY VALUE PROBLEM , 2018 .

[20]  Tomonari Suzuki,et al.  A new type of fixed point theorem in metric spaces , 2009 .

[21]  J. Jachymski,et al.  The contraction principle for mappings on a metric space with a graph , 2007 .

[22]  Poom Kumam,et al.  Some fixed point theorems concerning F-contraction in complete metric spaces , 2014, Fixed Point Theory and Applications.

[23]  Satish Shukla,et al.  Partial b-Metric Spaces and Fixed Point Theorems , 2014 .

[24]  E. Karapınar,et al.  Generalized contractions with triangular α-orbital admissible mapping on Branciari metric spaces , 2016, Journal of Inequalities and Applications.

[25]  Hassen Aydi,et al.  On fixed point results for a-implicit contractions in quasi-metric spaces and consequences , 2016 .

[26]  Qamrul Haq Khan,et al.  On Strong Coupled Coincidence Points ofg-Couplings and an Application , 2018, Journal of Function Spaces.

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

[28]  Hassen Aydi,et al.  On Common Fixed Points in the Context of Brianciari Metric Spaces , 2017 .

[29]  Radu Miculescu,et al.  New fixed point theorems for set-valued contractions in b-metric spaces , 2015, 1512.03967.

[30]  N. Shahzad,et al.  Some results on fixed points of α-ψ-Ciric generalized multifunctions , 2013 .

[31]  Hassen Aydi,et al.  Fixed points for α -admissible contractive mappings via simulation functions , 2016 .

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

[33]  Tayyab Kamran,et al.  An Approach to Existence of Fixed Points of Generalized Contractive Multivalued Mappings of Integral Type via Admissible Mapping , 2014 .

[34]  R. Baskaran,et al.  A note on the solution of a class of functional equations , 1986 .

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

[36]  D. O’Regan,et al.  Fixed Point Theory in Metric Type Spaces , 2016 .

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

[38]  E. Karapınar,et al.  Common fixed points for generalized $$\alpha $$α-implicit contractions in partial metric spaces: consequences and application , 2015 .

[39]  Masood Hussain Shah,et al.  KKM mappings in cone b-metric spaces , 2011, Comput. Math. Appl..

[40]  Richard Bellman,et al.  Functional equations in dynamic programming , 1978 .

[41]  Dariusz Wardowski,et al.  Fixed points of a new type of contractive mappings in complete metric spaces , 2012, Fixed Point Theory and Applications.

[42]  H. Piri,et al.  Generalized multivalued $F$-weak contractions on complete metric spaces , 2015 .