Quantum Calculus
Some Integral Inequalities Using Quantum Calculus Approach
... Abstract. The aim of this paper is to introduce a new class of preinvex functions which is called as generalized beta preinvex functions. We show that this class includes some other new classes of preinvex functions. We ...
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Integral inequalities via fractional quantum calculus
... quantum calculus. The derived results constitute contributions to the theory of integral inequalities and fractional calculus and can be specialized to yield numerous interesting fractional integral ...
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A Dunkl type generalization of Szász operators via post quantum calculus
... The object of this paper to construct Dunkl type Szász operators via post-quantum calculus. We obtain some approximation results for these new operators and compute convergence of the operators by using the ...
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Existence and quantum calculus of weak solutions for a class of two-dimensional Schrödinger equations in \(\mathbb{C}_{+}\)
... on the nonlinearity, we introduced a new type of quantum calculus via the Morse theory and variational methods. By applying the well-known Banach fixed point theorem in con- junction with the technique of ...
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Some results for Laplace type integral operator in quantum calculus
... Quantum calculus is a version of calculus where derivatives are differences and antideriva- tives are sums, and no further limits are ...The quantum calculus or q-calculus, ...
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New concepts of fractional quantum calculus and applications to impulsive fractional q difference equations
... In this paper we define new concepts of fractional quantum calculus by defining a new q-shifting operator. After giving the basic properties we define the q-derivative and q-integral. New definitions of ...
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Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus
... The main purpose of this paper is to introduce a generalized class of Dunkl type Szász operators via post quantum calculus on the interval [ 1 2 , ∞). This type of modification allows a better estimation of ...
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Quantum calculus on finite intervals and applications to impulsive difference equations
... Quantum calculus is the modern name for the investigation of calculus without ...The quantum calculus or q-calculus began with FH Jackson in the early twentieth century, but this ...
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New Poisson–Sch type inequalities and their applications in quantum calculus
... Vargas-De-Teón (J. Inequal. Appl. 2017:114, 2017), are generalized by using Poisson identities involving modified Poisson kernel functions with respect to a cone. New generalizations of improved Poisson–Sch type ...
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New Integral Inequalities in Quantum Calculus
... N.T., Integral inequalities of Gr¨ uss type via P´ olya-Szeg¨ o and Shisha-Mond results, East Asian Math.. R., Basic Hypergeometric Series , 2nd Edition, (2004), Encyclopedia of Mathemat[r] ...
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Existence and uniqueness of solutions for multi term fractional q integro differential equations via quantum calculus
... fractional calculus and q-calculus are one of the significant branches in mathematical ...q-fractional calculus can be found in [9], as indicated: Perhaps Leibniz did not expect this number of ...
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On Some Inequalities of Uncertainty Principles Type in Quantum Calculus
... 2007, to state local uncertainty principles for the q-Fourier-cosine, the q-Fourier-sine, and the q-Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for t[r] ...
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Applications of quantum calculus on finite intervals to impulsive difference inclusions
... tum calculus. In recent years, the topic of q-calculus has attracted the attention of several researchers and a variety of new results can be found in the papers [–] and the refer- ences cited ...
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Research on Some New Results Arising from Multiple q-Calculus
... q-di¤erence calculus (or the so-called quantum calculus), which is an old ...is, quantum calculus (also known as q-calculus) was one of the most active area of research in the ...
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Some q-analogues of Hermite–Hadamard inequality of functions of two variables on finite rectangles in the plane
... Sudsutad, W., Ntouyas, S.K., Tariboon, J., 2015. Quantum integral inequalities for convex functions. J. Math. Inequal. 9 (3), 781–793. Tariboon, J., Ntouyas, S.K., 2013. Quantum calculus on finite ...
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A certain \((p,q)\) derivative operator and associated divided differences
... The quantum calculus has many applications in the fields of special functions and many other areas (see ...post- quantum calculus denoted by the (p, ...of quantum calculus cannot ...
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Quantum integral inequalities on finite intervals
... In this paper, some of the most important integral inequalities of analysis are extended to quantum calculus. These include the Hölder, Hermite-Hadamard, trapezoid, Ostrowski, Cauchy-Bunyakovsky-Schwarz, ...
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A Study on New q Integral Inequalities
... The q-Jackson integral and q-derivative are related by the “fundamental theorem of quantum calculus” which can be restated [3, p.73] as follows: If F is an anti q-derivative of the funct[r] ...
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Oscillation theorems for higher order neutral nonlinear dynamic equations on time scales
... The theory of time scales was introduced by Hilger [1] in order to unify, extend and generalize ideas from discrete calculus, quantum calculus and continuous calculus to arbitrary time scale ...
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A general quantum difference calculus
... The quantum calculus is known as the calculus without ...a quantum difference operator which allows to deal with sets of nondiffer- entiable ...functions. Quantum difference operators have ...
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