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Solution to Fredholm integral inclusions via ( F, δ b )-contractions

100%

Nashine H. K. , Agarwal R. P. , Kadelburg Z.

Open Mathematics

2016

tom 14

nr 1

1053-1064

We present sufficient conditions for the existence of solutions of Fredholm integral inclusion equations using new sort of contractions, named as multivalued almost F -contractions and multivalued almost F -contraction pairs under ı-distance, defined in b-metric spaces. We give its relevance to fixed point results in orbitally complete b-metric spaces. To rationalize the notions and outcome, we illustrate the appropriate examples.

Multivalued fractals in b-metric spaces

86%

Boriceanu M. , Bota M. , Petruşel A.

Open Mathematics

2010

tom 8

nr 2

367-377

Fractals and multivalued fractals play an important role in biology, quantum mechanics, computer graphics, dynamical systems, astronomy and astrophysics, geophysics, etc. Especially, there are important consequences of the iterated function (or multifunction) systems theory in several topics of applied sciences. It is known that examples of fractals and multivalued fractals are coming from fixed point theory for single-valued and multivalued operators, via the so-called fractal and multi-fractal operators. On the other hand, the most common setting for the study of fractals and multi-fractals is the case of operators on complete or compact metric spaces. The purpose of this paper is to extend the study of fractal operator theory for multivalued operators on complete b-metric spaces.

A fixed point result for φ-contractions on b-metric spaces without the boundedness assumption

86%

Păcurar M.

2010

tom Nr 43

127-137

Starting from a result in [V. Berinde,Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory (Preprint), "Babeş-Bolyai" University of Cluj-Napoca, 3 (1993), 3-9 ], we prove the existence and uniqueness of the fixed points for φ-contractions on b-metric spaces. We also build a theory of this fixed point result.

Stability of iterative procedures for multivalued maps in metric spaces

72%

Singh S. , Bhatnagar C. , Mishra S.

2005

tom Vol. 38, nr 4

905-916

Let (X,d) be a metric space and T a self-map of X. Let Xn+i = f(T,Xn) denote some iterative procedure. Let {xn} be convergent to a fixed point u of T and {yn} be an arbitrary sequence in X. Set En=d[yn+i, f(T, yn)], n = 0,1,2,..., then the iterative procedure f(T,Xn) is T-stable provided that limEn = 0 implies that limnyn = u. This definition has been extended by Singh and Chadha [34] to discuss the problem of stability for multivalued operators on metric spaces. The purpose of this paper is to present a fixed point theorem for generalized multivalued contractions on a setting more general than metric spaces. The same is utilized to discuss the problem of stability of iterative procedures in multivalued analysis. Some special cases due to Stefan Czerwik and others are discussed as special cases.