Some new common fixed point results for generalized contractive multi-valued non-self-mappings

In this work, we study some new common fixed point results for generalized contractive multi-valued non-self-mappings on complete metric spaces.     

The fixed point index for compact absorbing contractive admissible maps

An index theory is presented for compact (and more generally compact absorbing contractive) Ads (and more generally Ad) maps.     

Common fixed point theorems for some new generalized contractive type mappings

In this paper, some new generalized contractive type conditions for a pair of mappings in metric space are defined. Some common fixed point results for these mappings are presented.     

Some generalizations of Caristi’s fixed point theorem with applications to the fixed point theory of weakly contractive set-valued maps and the minimization problem

In this paper, we first prove some generalizations of Caristi’s fixed point theorem. Then we give some applications to the fixed point theory of weakly contractive set-valued maps and the minimization problem.     

A common fixed point theorem for compatible quasi contractive self mappings in metric spaces

A common fixed point theorem for weakly commuting quasi contractive self mappings with contracting orbital diameters in metric spaces [V. Berinde, A common fixed point theorem for quasi contractive type mappings, Ann. Univ. Sci. Budapest. 46 (2003) 81-90] is extended to the more general class of compatible quasi contractive self mappings. Our result does extend and generalize numerous related results in literature.     

Fixed point theory for compact absorbing contractive admissible type maps

In this article we present new Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Fréchet spaces. Also, we discuss condensing maps with a compact attractor. Finally we present new antipodal fixed point theory for Kakutani maps.     

Common fixed point of generalized weakly contractive maps in partial metric spaces

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized (φ,ψ)-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.     

Common fixed point theorems of Gregus type for weakly compatible mappings satisfying generalized contractive conditions

We prove a common fixed point theorem of Gregus type for four mappings satisfying a generalized contractive condition in metric spaces using the concept of weak compatibility which generalizes theorems of [I. Altun, D. Turkoglu, B.E. Rhoades, Fixed points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), article ID 17301; A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378; A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (1) (2007) 31-45; P. Vijayaraju, B.E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15 (2005) 2359-2364; X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl. 333 (2) (2007) 780-786]. We prove also a common fixed point theorem which generalizes Theorem 3.5 of [H.K. Pathak, M.S. Khan, T. Rakesh, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. 53 (2007) 961-971] and common fixed point theorems of Gregus type using a strict generalized contractive condition, a property (E.A) and a common property (E.A).     

Random fixed points of discontinuous random maps

We prove some random fixed-point theorems for random maps which are not necessarily continuous. This may lead to the discovery of some new results in random fixed-point theory for discontinuous maps.     

Fixed point theory for extension type maps in topological spaces

Several new fixed point results for self maps in extension type spaces are presented in this article.     

Asymptotic Lefschetz fixed point theory for ANES(compact) maps

A number of new Lefschetz fixed point theorems are established for ANES(compact) maps. Also compact absorbing contraction maps are discussed.      

Common fixed point theorems for maps under a contractive condition of integral type

Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007-4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149-153].     

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.     

On coincidence point and fixed point theorems for nonlinear multivalued maps

Several characterizations of MT-functions are first given in this paper. Applying the characterizations of MT-functions, we establish some existence theorems for coincidence point and fixed point in complete metric spaces. From these results, we can obtain new generalizations of Berinde-Berinde?s fixed point theorem and Mizoguchi-Takahashi?s fixed point theorem for nonlinear multivalued contractive maps. Our results generalize and improve some main results in the literature.     

Fixed point theorems for generalized metrically inward maps

We prove fixed point results for multimaps satisfying a generalized metric (or an α-metric) inwardness condition. Our results extend, generalize or improve several known results.     

On fixed point linear equations

Summary By means of successive partial substitutions it is possible to obtain new fixed point linear equations from old ones and it is interesting to determine how the spectral radius of the corresponding matrices varies. We prove that, when the original matrix is nonnegative, this variation is decreasing or increasing, depending on whether the original matrix has its spectral radius smaller or greater than 1. We answer in this way a question posed by F. Robert in [5].     

Coupled common fixed point results in two generalized metric spaces

In this paper, study of necessary conditions for the existence of unique coupled common fixed point of contractive type mappings in the context of two generalized metric spaces is initiated. These results generalize several comparable results from the current literature. We also provide illustrative examples in support of our new results.