There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Some Results on Fixed Points

We present a fixed point theorem for generalized -Meir-Keeler type contractions in the setting of generalized -metric spaces. The presented results improve, generalize, and unify many existing famous results in the corresponding literature.

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-Meir-Keeler Contraction Mappings in Generalized -Metric Spaces

Preface 1 Contradictions 2 Non-expansive maps 3 Continuation methods for contractive and non-expansive mapping 4 The theorems of Brouwer, Svhauder and Monch 5 Non-linear alternatives of Leray-Schauder type 6 Continuation principles for condensing maps 7 Fixed point theorems in conical shells 8 Fixed point theory in Hausdorff locally convex linear topological spaces 9 Contractive and non-expansive multivalued maps 10 Multivalued maps with continuous selections 11 Multivalued maps with closed graph 12 Degree theory Bibliography Index

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Fixed Point Theory and Applications

C 1 Abstract. We present a survey of flxed point results in generalized metric spaces (g.m.s.) in the sense of Branciari (Branciari, A., (2000), A flxed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57, 31{37). Since it may happen that the topology of such space is not Hausdorfi, several authors added Hausdorfness (or some other condition) as an additional assumption in order to obtain their results. We show here that such assumptions are usually super∞uous. Finally, we state some open questions on the topic.

On generalized metric spaces: a survey

In this paper, we establish that every controlled metric space $(X, d_{\alpha })$ induces a Hausdorff controlled metric $(\textit{H}_{\alpha }, \textit{CLD}(X))$ on the class of closed subsets of X which is also complete if $(X, d_{\alpha })$ is complete. Furthermore, we define multivalued almost F-contractions on Hausdorff controlled metric spaces and prove some fixed point results.

/pdf/fixed-point-results-via-a-hausdorff-controlled-type-metric-186mwzqhq3.pdf

Fixed point results via a Hausdorff controlled type metric

The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and some other authors and to prove some new coupled fixed point theorems for contractive mappings involving new function classes in complete metric space endowed with a partial order. Our theorems can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

/pdf/coupled-fixed-point-theorems-for-contractive-mappings-1wax6jjne7.pdf

Coupled Fixed Point Theorems for Contractive Mappings Involving New Function Classes and Applications

In this article, we establish some fixed point theorems for weakly contractive mappings defined in ordered metric-like spaces. We provide an example and some applications in order to support the useability of our results. These results generalize some well-known results in the literature. We also derive some new fixed point results in ordered partial metric spaces.

/pdf/fixed-point-theorems-for-weakly-contractive-mappings-in-2lax90t583.pdf

Fixed point theorems for weakly contractive mappings in partially ordered metric-like spaces

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M q ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M q ( x , y , t ) ∗ M q ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

Fuzzy double controlled metric spaces and related results

Abstract In this study, we develop the concept of multivalued Suzuki-type θ-contractions via a gauge function and established two new related fixed point theorems on metric spaces. We also discuss an example to validate our results.

/pdf/on-multivalued-suzuki-type-th-contractions-and-related-l1px23wxej.pdf

Hüseyin Işık

Papers

Fixed point results via a Hausdorff controlled type metric

Coupled Fixed Point Theorems for Contractive Mappings Involving New Function Classes and Applications

Fixed point theorems for weakly contractive mappings in partially ordered metric-like spaces

Fuzzy double controlled metric spaces and related results

On multivalued Suzuki-type θ-contractions and related applications