scholarly journals Locally constant constructive functions and connectedness of intervals

2020 ◽  
Vol 30 (7) ◽  
pp. 1425-1428
Author(s):  
Viktor Chernov
Keyword(s):  
Disjoint Union ◽  
Related Result ◽  
Constant Function ◽  
Real Numbers ◽  
Constructive Function

Abstract We prove that every locally constant constructive function on an interval is in fact a constant function. This answers a question formulated by Andrej Bauer [ 1]. As a related result, we show that an interval consisting of constructive real numbers is in fact connected but can be decomposed into the disjoint union of two sequentially closed nonempty sets.

The unprovability in intuitionistic formal systems of the continuity of effective operations on the reals

1976 ◽  
Vol 41 (1) ◽  
pp. 18-24
Author(s):  
Michael Beeson
Keyword(s):  
Present Note ◽  
Baire Space ◽  
Philosophical Analysis ◽  
Real Numbers ◽  
The Real ◽  
Formal Systems ◽  
Constructive Function ◽  
Effective Operation

The question of continuity of functions defined on Baire space NN or on the reals has been of great interest to constructivists. We have little hope of answering the question without a fundamental philosophical analysis of the notion of constructive function. However, one can ask whether the continuity of functions can be derived in known intuitionistic formal systems, and answer these questions by mathematical means.The constructivist does not generally wish to restrict himself to reals (or members of NN) given by a recursive law; therefore the most natural formal systems have variables for reals, sequences and functions. The axioms of these systems turn out to be compatible with the assumption that every real or sequence is given by a recursive law, and every function by an effective operation. An underivability result, therefore, is only strengthened if this assumption is taken as an axiom; and once this is done, we may as well work with (indices of) effective operations, within arithmetic.By KLS is meant the assertion that each effective operation on Baire space NN is continuous. In [B1] it is shown that this statement cannot be proved in various intuitionistic formal systems. The continuity of functions on the reals has been of even greater interest to constructivists than the continuity of functions on NN; by KLS(R) is meant the assertion that each effective operation from the real numbers R to R is continuous. It is the purpose of the present note to show that KLS(R) is also underivable in intuitionistic formal systems.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

Dynamics of a family of orbitally continuous mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3507-3517
Author(s):  
Abhijit Pant ◽  
R.P. Pant ◽  
Kuldeep Prakash
Keyword(s):  
Fixed Points ◽  
Julia Sets ◽  
Real Numbers ◽  
Continuous Mappings ◽  
Non Linear

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5945-5953 ◽  
Author(s):  
İmdat İsçan ◽  
Sercan Turhan ◽  
Selahattin Maden
Keyword(s):  
Convex Functions ◽  
Real Numbers ◽  
Absolute Value ◽  
Special Means ◽  
Quasi Convexity

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

On calculating extinction probabilities for branching processes in random environments

1969 ◽  
Vol 6 (03) ◽  
pp. 478-492 ◽  
Author(s):  
William E. Wilkinson
Keyword(s):  
Generating Functions ◽  
Infinite Sequence ◽  
Branching Processes ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Random Environments ◽  
Real Numbers ◽  
Discrete Time Markov Chain ◽  
Extinction Probabilities ◽  
Image Position

Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.

scholarly journals Some Properties Involving q-Hermite Polynomials Arising from Differential Equations and Location of Their Zeros

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1168
Author(s):  
Cheon Seoung Ryoo ◽  
Jung Yoog Kang
Keyword(s):  
Differential Equations ◽  
Hermite Polynomials ◽  
Real Numbers ◽  
Different Types

Hermite polynomials are one of the Apell polynomials and various results were found by the researchers. Using Hermit polynomials combined with q-numbers, we derive different types of differential equations and study these equations. From these equations, we investigate some identities and properties of q-Hermite polynomials. We also find the position of the roots of these polynomials under certain conditions and their stacked structures. Furthermore, we locate the roots of various forms of q-Hermite polynomials according to the conditions of q-numbers, and look for values which have approximate roots that are real numbers.

A variation on Nθ ward continuity

2020 ◽  
Vol 27 (2) ◽  
pp. 191-197 ◽  
Author(s):  
Huseyin Cakalli ◽  
Mikail Et ◽  
Hacer Şengül
Keyword(s):  
Real Numbers

AbstractThe main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of sequences of real numbers. Strongly ideal lacunary ward continuity is also investigated. Interesting results are obtained.

scholarly journals Powers: The No-Successor Problem

2021 ◽  
pp. 1-18
Author(s):  
JOHN PEMBERTON
Keyword(s):  
Continuous Time ◽  
Real Numbers ◽  
Causal Relations

Abstract This essay considers the implications for the powers metaphysic of the no-successor problem: As there are no successors in the set of real numbers, one state cannot occur just after another in continuous time without there being a gap between the two. I show how the no-successor problem sets challenges for various accounts of the manifestation of powers. For powers that give rise to a manifestation that is a new state, the challenge of no-successors is similar to that faced on Bertrand Russell's analysis by causal relations. Powers whose manifestation is a processes and powers that manifest through time (perhaps by giving rise to changing through time) are challenged differently. To avoid powers appearing enigmatic, these challenges should be addressed, and I point to some possible ways this might be achieved. A prerequisite for addressing these challenges is a careful focus on the nature and timing of the manifesting and manifestation of powers.

Real Numbers

2020 ◽  
pp. 1-52
Author(s):  
Nicolas A. Pereyra
Keyword(s):  
Real Numbers
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