Convergence Estimates for Gupta-Srivastava Operators

The Grüss-Voronovskaya-type approximation results for the modified Gupta-Srivastava operators are considered. Moreover, the magnitude of differences of two linear positive operators defined on an unbounded interval has been estimated. Quantitative type results are established as we initially obtain the moments of generalized discrete operators and then estimate the difference of these operators with the Gupta-Srivastava operators.

Voronovskaja’s theorem for functions with exponential growth

In the present paper we establish a general form of Voronovskaja’s theorem for functions defined on an unbounded interval and having exponential growth. The case of approximation by linear combinations is also considered. Applications are given for some Szász–Mirakyan and Baskakov-type operators.

Measures of noncompactness and superposition operator in the space of regulated functions on an unbounded interval

In this paper, we formulate necessary and sufficient conditions for relative compactness in the space $$BG({\mathbb {R}}_+,E)$$ B G ( R + , E ) of regulated and bounded functions defined on $${\mathbb R}_+$$ R + with values in the Banach space E. Moreover, we construct four new measures of noncompactness in the space $$BG({\mathbb {R}}_+,E)$$ B G ( R + , E ) . We investigate their properties and we describe relations between these measures. We provide necessary and sufficient conditions so that the superposition operator (Niemytskii) maps $$BG({\mathbb {R}}_+,E)$$ B G ( R + , E ) into $$BG({\mathbb {R}}_+,E)$$ B G ( R + , E ) and, additionally, be compact.

Spectral Theory of Singular Hahn Difference Equation of the Sturm-Liouville Type

In this work, we consider the singular Hahn difference equation of the Sturm-Liouville type. We prove the existence of the spectral function for this equation. We establish Parseval equality and an expansion formula for this equation on a semi-unbounded interval.

Global attracting solutions to Hilfer fractional differential inclusions of Sobolev type with noninstantaneous impulses and nonlocal conditions

In this paper, we establish the existence of decay mild solutions on an unbounded interval of nonlocal fractional semilinear differential inclusions with noninstantaneous impulses and involving the Hilfer derivative. Our argument uses fixed point theorems, semigroup theory, multi-functions and a measure of noncompactness on the space of piecewise weighted continuous functions defined on an unbounded interval. An example is provided to illustrate our results.

β–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System

In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the β –Ulam stability, β –Hyers–Ulam stability and β –Hyers–Ulam–Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Grönwall type inequality and evolution family as a basic tool for our results. We present an example to demonstrate the application of the main result.

Generalized Bernstein type operators on unbounded interval and some approximation properties

In the present paper, we construct a new family of Bernstein type operators on infinite interval by using exponential function ax. We study some approximation results for these new operators on the interval [0,1).