θ-ϕ-Contraction on α, η-Complete Rectangular b-Metric Spaces

In this paper, we present some fixed point results for generalized contraction in the framework of compete rectangular metric spaces. Further, we establish some fixed point theorems for this type of mappings defined on such spaces. Our results generalize and improve many of the well-known results. Moreover, to support our main results, we give an illustrative example.

[1]  Nawab Hussain,et al.  Fixed Point Theory in -Complete Metric Spaces with Applications , 2014 .

[2]  I. Ramabhadra Sarma,et al.  CONTRACTIONS OVER GENERALIZED METRIC SPACES , 2009 .

[3]  Chi-Ming Chen,et al.  Periodic Points and Fixed Points for the Weaker (ϕ, φ)-Contractive Mappings in Complete Generalized Metric Spaces , 2012, J. Appl. Math..

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

[5]  Dingwei Zheng,et al.  New fixed point theorems for θ-φ contraction in complete metric spaces , 2017 .

[6]  Cristina Di Bari,et al.  Common fixed points in generalized metric spaces , 2012, Appl. Math. Comput..

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

[8]  A Branciari,et al.  A fixed point theorem of Banach--Caccioppoli type on a class of generalized metric spaces , 2000, Publicationes Mathematicae Debrecen.

[9]  William A. Kirk,et al.  Generalized metrics and Caristi’s theorem , 2013, Fixed Point Theory and Applications.

[10]  P. Das.  A FIXED POINT THEOREM ON A CLASS OF GENERALIZED METRIC SPACES , 2002 .

[11]  S. Yum.  A HOPF BIFURCATION IN A MULTIPLE FREE BOUNDARY PROBLEM , 2001 .

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

[13]  Vahid Parvaneh,et al.  New fixed point results in b-rectangular metric spaces , 2016 .

[14]  Y. Cho,et al.  Fixed point results for generalized Theta-contractions , 2017 .