On the Correlation between Banach Contraction Principle and Caristi’s Fixed Point Theorem in b-Metric Spaces

We solve a question posed by E. Karapinar, F. Khojasteh and Z.D. Mitrović in their paper “A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces”. We also characterize the completeness of b-metric spaces with the help of a variant of the contractivity condition introduced by the authors in the aforementioned article.

Some Applications of New Complex Function Space Constructed by Different Weights and Exponents

In this article, we develop and study a new complex function space formed by varying the weights and exponents under a definite function. We investigate the geometric and topological characteristics of mapping ideals created using s -numbers and this complex function space. Also, the action of shift mappings on this complex function space has been discussed. Finally, we introduced an extension of Caristi’s fixed point theorem on it.

A Generalization of Caristi’s Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space

Suppose p n be sequence of positive reals. By H w p n , we represent the space of all formal power series ∑ n = 0 ∞ a n z n equipped with ∑ n = 0 ∞ λ a n / n + 1 p n < ∞ , for some λ > 0 . Various topological and geometric behavior of H w p n and the prequasi ideal constructs by s -numbers and H w p n have been considered. The upper bounds for s -numbers of infinite series of the weighted n -th power forward shift operator on H w p n with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi’s fixed point theorem in H w p n .

Caristi’s Fixed Point Theorem in G-Metric Spaces and Applications

In this paper, we give some versions of Caristi’s fixed point theorem in a more general metric spacesetting. Our work extends a good number of results in this area of research

On Caristi’s fixed point theorem in metric spaces with a graph

We generalize the Caristi’s fixed point theorem for single valued as well as multivalued mappings defined on ametric space endowed with a graph andw-distance. Particularly, we modify the concept of the (OSC)-propertydue to Alfuraidan and Khamsi (Alfuraidan M. R. and Khamsi, M. A.,Caristi fixed point theorem in metric spaceswith graph, Abstr. Appl. Anal., (2014) Art. ID 303484, 5.) which enable us to reformulated their stated graphtheory version theorem (Theorem 3.2 in Alfuraidan M. R. and Khamsi, M. A.,Caristi fixed point theorem in metricspaces with graph, Abstr. Appl. Anal., (2014) Art. ID 303484, 5. ) to the case ofw-distance. Consequently,we extend and improve some recent works concerning extension of Banach Contraction Theorem tow-distancewith graph e.g. (Jachymski, J.,The contraction principle for mappings on a metric space with graph, Proc. Amer. Math.Soc.,136(2008), No. 4, 1359–1373; Nieto, J. J., Pouso, R. L. and Rodriguez-Lopez R.,Fixed point theorems in orderedabstract spaces, Proc. Amer. Math. Soc.,135(2007), 2505–2517 and Petrusel, A. and Rus, I.,Fixed point theorems inorderedL−spaces endowed with graph, Proc. Amer, Math. Soc.,134(2006), 411–418.