Fixed point of contractive mappings in generalized metric spaces

We prove a fixed point theorem for contractive mappings of Boyd and Wong type in generalized metric spaces, a concept recently introduced in [BRANCIARI, A.: A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen 57 (2000), 31–37].      

Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings

In this paper, the famous Banach contraction principle and Caristi's fixed point theorem are generalized to the case of multi-valued mappings. Our results are extensions of the well-known Nadler's fixed point theorem [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475-487], as well as of some Caristi type theorems for multi-valued operators, see [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188; J.P. Aubin, Optima and Equilibria. An Introduction to Nonlinear Analysis, Grad. Texts in Math., Springer-Verlag, Berlin, 1998, p. 17; S.S. Zhang, Q. Luo, Set-valued Caristi fixed point theorem and Ekeland's variational principle, Appl. Math. Mech. 10 (2) (1989) 111-113 (in Chinese), English translation: Appl. Math. Mech. (English Ed.) 10 (2) (1989) 119-121], etc.     

Cone metric spaces and fixed point theorems in diametrically contractive mappings

In this paper, some topological concepts and definitions are generalized to cone metric spaces. It is proved that every cone metric space is first countable topological space and that sequentially compact subsets axe compact. Also, we define diametrically contractive mappings and asymptotically diametrically contractive mappings on cone metric spaces to obtain some fixed point theorems by assuming that our cone is strongly minihedral.     

Cone metric spaces and fixed point theorems of contractive mappings

In this paper we introduce cone metric spaces, prove some fixed point theorems of contractive mappings on cone metric spaces.     

Approximating fixed points of a pair of contractive type mappings in generalized convex metric spaces

In this paper, we consider an Ishikawa type iteration process with errors, which converges to the unique common fixed point of a pair of contractive type mappings in complete generalized convex metric spaces. Furthermore, we obtain the corresponding results in Banach spaces. Our results extend and generalize many known results.     

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.     

Continuation method for -sublinear mappings

Let be a real Banach space partially ordered by a closed convex cone with nonempty interior . We study the continuation method for the monotone operator which satisfies

for all , , where . Thompson's metric is among the main tools we are using.     

锥Pf的若干性质

利用实赋范线性空间E上非零连续线性泛函f,确定了E上半序关系和锥Pf,证明了锥Pf的几个性质,给出了H ilbert空间中Pf的对偶锥的表现形式及由Pf确定的H ilbert投影距离与T hom pson距离.     

BOUNDARY VALUE PROBLEM FOR NONLINEAR IMPULSIVE INTEGRO-DIFFERENTIAL EQUATION IN BANACH SPACE

In this paper, by establishing a new comparison result and using the monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problem for second-order impulsive differential equation which depends on x' in Banach space is obtained.     

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).     

Periodic solutions of difference equations

We give an overview of results on the existence of periodic solutions of difference equations that have been obtained in the last two decades. The survey covers both ordinary and Volterra difference systems. Some extensions and generalizations of known result are also presented.     

Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces

In this paper we introduce the concept of a tripled coincidence point for a pair of nonlinear contractive mappings F : X³ → X and g : X → X. The obtained results extend recent coincidence theorems due to ?iri? and Lakshmikantham [V. Lakshmikantham, L. ?iri?, L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009) 4341-4349].     

Some fixed point theorems for non-self mappings of contractive type with applications to endpoint theory

In this paper, in the setting of complete metric spaces we establish some fixed point theorems for non-self mappings of contractive type satisfying either the Reich–Zaslavski property or the approximate fixed point property. As applications, we obtain some results in endpoint theory.     

On entire solutions of some type of nonlinear difference equations

In this article, the existence of finite order entire solutions of nonlinear difference equations f~n+ P_d(z, f) = p_1 e~(α1 z)+ p_2 e~(α2 z) are studied, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial in f of degree d(≤ n-2), p_1, p_2 are small meromorphic functions of ez, and α_1, α_2 are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions.     

Some common fixed point theorems for selfmappings satisfying two contractive conditions of integral type in a uniform space

In this paper, we establish some common fixed point theorems for selfmappings of a uniform space by employing both the concepts of an A—distance and an E—distance introduced by Aamri and El Moutawakil [1] and two contractive conditions of integral type. Our results are generalizations and extensions of the classical Banach’s fixed point theorem of [2, 3, 19], some results of Aamri and El Moutawakil [1], Theorem 2.1 of Branciari [5] as well as a result of Jungck [7].      

Nonlinear equations based on jointly homogeneous mappings

In this paper, we consider a nonlinear equation based on two-variable monotone and jointly homogeneous functions on an open convex normal cone

x=g(h(a,x),k(b,x))     

Unique common fixed point of a family of self-maps with same type contractive condition in 2-metric space

In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if (i) {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; (ii) Tm,μ· Tn,ν = Tn,ν· Tm,μ for all m,n,μ,ν∈ N with μ = ν. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.     

Minimal universal denominators for linear difference equations

We provide minimal universal denominators for linear difference equations with fixed leading and trailing coefficients. In the case of first-order equations, they are factors of Abramov's universal denominators. While in the case of higher order equations, we show that Abramov's universal denominators are minimal.     

A result concerning the stability of some difference equations and its applications

In this paper, we investigate the Hyers-Ulam stability problem for the difference equation f(x +p, y +q)- φ(x, y)f(x, y)- ψ(x, y)= 0. An erratum to this article is available at .