We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

Results on common fixed points for pairs of single and multivalued mappings on a complete metric space are examined. Our work establishes a common fixed point theorem for a pair of generalized contraction self-maps and a pair of set-valued mappings.

B. Damjanovi? and D. Dori?, Multivalued generalizations of the Kannan fixed point theorem, Filomat , vol. 25 (1) , DOI: 10. 2298/FIL 1101125D, (2011), 125-131. B. E. Rhoades and M. Abbas, Maps satisfying generalized contractive condition of integral type for which F(T) = F(Tn), International Journal of Pure and Applied Mathematics, vol. 45, no. 2 (2008), 225-231. D. Dori? and R. Lazovi?, Some S...

In this paper, a generalization of Nadler’s fixed point theorem is presented for H-type k-multivalued weak contractive mappings. We consider a nonconvex Hammerstein type integral inclusion and prove an existence theorem by using an H-type multi-valued weak contractive mapping.

where F : J ×Rn → (Rn) is a multivalued map, (Rn) is the family of all subsets of Rn, y0 ∈ Rn, and 0 ≤ t1 < t2 < ··· < tp ≤ b, p ∈ N, ck = 0, k = 1,2, . . . , p. The single-valued case of problem (1.1) was studied by Byszewski [5], in which a new definition of mild solution was introduced. In the same paper, it was remarked that the constants ck, k = 1, . . . , p, from condition (1.1b) can sati...

In this paper we study the existence of global weak solutions for a hyperbolic differential inclusion with a discontinuous and nonlinear multivalued term. Also we investigate the asymptotic behavior of solutions.