“Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.

SET-Valued Analysis

Some Results on Fixed Points

We prove some common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces both in the sense of Kramosil and Michalek and in the sense of George and Veeramani by using the new property and give some examples Our results improve and generalize the main results of Mihet in (Mihet, 2010) and many fixed point theorems in fuzzy metric spaces

https://downloads.hindawi.com/journals/jam/2011/637958.pdf

Common Fixed Point Theorems for a Pair of Weakly Compatible Mappings in Fuzzy Metric Spaces

We obtain two fixed point theorems for a class of operators called occasionally weakly compatible maps defined on a symmetric space . These results establish two of the most general fixed point theorems for four maps.

http://www.math.ubbcluj.ro/~nodeacj/download.php?f=062rhoadesABS.pdf

Fixed point theorems for occasionally weakly compatible mappings

Preface On the Semilocal Convergence of Newton's Method Under Unifying Conditions Inequalities and Fixed Points in Menger Convex Metric Spaces Applications of the Perov's Fixed Point Theorem to Delay Integro-Differential Equations On Vector Equilibrium Problems with Multifunctions Fixed Points in Generalised Metric Spaces and the Stability of a Cubic Functional Equation Continuous Selection and Coincidence Theorems on Product G-Convex Space Sensitivity Analysis of Solution Set for a New Class of Generalised Implicit Quasi-Variational Inclusions Fixed Points in Probabilistic-Quasi-Metric Spaces Common Fixed Point Theorems for Condensed Mappings The Strongly Convergence Theorems of Fixed Points for Local Strictly F-Pseudocontractive On Generalised Non-linear Variational Inequalities A Note on a Paper of Hadic and Pap The Ishiwaka and Mann Iteration Methods On Certain Applications of Leray-Schauder Alternate Remarks on Concepts of Generalised Convex Spaces Generic Existence and Non-Existence of Approximate Fixed Points General System of Relaxed g-?-r-Pseudococoercive Non-linear Variational Inequalities and Projection Methods Three-Step Iteration Methods with Errors for Non-expansive Mappings in Uniformly Convex Banach Spaces On Nonnegative Linear Composite Games of NTU-Game Probabilistic Contractor and Non-linear Operator Equations with Set-Valued Operator in Probabilistic Normed Spaces Index.

Fixed Point Theory and Applications

Some new common fixed point theorems under strict contractive conditions

The main purpose of this paper is to obtain several common fixed point theorems for contractive or expansive self-mappings of uniform spaces.

/pdf/common-fixed-point-theorems-for-e-contractive-or-e-expansive-2w30ciohrs.pdf

Common fixed point theorems for E-contractive or E-expansive maps in uniform spaces.

In this paper, we prove a common fi xed point theorem in symmetric spaces for weakly compatible maps without appeal to continuity, which generalizes the result of Hicks and Rhoades (1). At the end, we give an application of our main Theorem to probabilistic spaces.

/pdf/common-fixed-points-for-weakly-compatible-maps-in-symmetric-40tlhcxzuq.pdf

Common fixed points for weakly compatible maps in symmetric spaces with application to probabilistic 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.

/pdf/th-ph-contraction-on-a-e-complete-rectangular-b-metric-4c4v4482as.pdf

Mohamed Aamri

Papers

Some new common fixed point theorems under strict contractive conditions

Common fixed point theorems for E-contractive or E-expansive maps in uniform spaces.

Common fixed points for weakly compatible maps in symmetric spaces with application to probabilistic spaces

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

Fixed points and variational principle in uniform spaces.